Supersymmetric Yang-Mills Theories in $D\ge 12$

TL;DR

This paper develops supersymmetric Yang-Mills theories in arbitrary even dimensions beyond ten, using null-vector techniques and projection operators, potentially enabling consistent supergravity theories in higher dimensions.

Contribution

It generalizes supersymmetric Yang-Mills theories to any even dimension beyond ten, overcoming previous obstructions with new projection methods.

Findings

Formulation of supersymmetric Yang-Mills in arbitrary even dimensions

Use of null-vectors and projection operators to overcome dimensional obstructions

Implication for consistent supergravity theories in higher dimensions

Abstract

We present supersymmetric Yang-Mills theories in arbitrary even dimensions with the signature (9+m,1+m) where $m=0,1,2,...$ beyond ten-dimensions up to infinity. This formulation utilizes null-vectors and is a generalization of our previous work in 10+2 dimensions to arbitrary even dimensions with the above signature. We have overcome the previously-observed obstruction beyond 11+3 dimensions, by the aid of projection operators. Both component and superspace formulations are presented. This also suggests the possibility of consistent supergravity theories in any even dimensions beyond 10+1 dimensions.